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Cypecad , considera a diferencia de otros programas, el tamao de los elementos( vigas, pilares, losas etc) , es decir que para Cypecad el que una viga llegue excentrica a un pilar le provocar que aparezcan momentos en este ltimo aunque la conexi

CYPECAD, unlike other programs takes into account the size of the elements of the structure (beams, columns, slabsetc). Therefore, if a beam reaches a column eccentrically, this will cause moments to arise even though the intersection node consists of a pinned connection. The influence of this eccentricity on the results obtained can be seen in the practical example described below.

Example 1.

Two frames consisting of two 0.50x0.50m columns and a 0.25x0.50m simply supported beam. The beam is placed centrally with respect to the columns in one case and displaced in the other.

Both frames have an applied line load of 20 kN/m (live load). Once the analysis has concluded, the reactions at the columns differ; the columns with the eccentric beam have an My > 0 kNm. If this moment is analysed, it can be seen that it is due to the eccentricity of the load transmitted by the beam to the column.

The live load applied on the beam equals 20 kN/m. The beam measures 5m, hence the load on each column (without applying safety factors) is 20 x 5/2 ( 50kN. The eccentricity of the other beam with respect to the column is 0.5/2 - 0.25/2 = 0.125m. Therefore the moment due to the eccentric beam is:

My = 50 x 0.125 = 6.25kNm.

CYPECAD undertakes a series of considerations when discretising and generating the structures self weight. Beam lengths correspond to the lengths between the internal faces of columns, hence if the beams are wider than the columns, the weight of the beam surpassing the internal face of the columns is not considered. As for the columns, the program considers the free height of the column as the column height; the part of the column intersecting with the beam is taken as being a rigid and non-deformable node.

The discretisation carried out by the program can be seen with the following option: Results tab > Envelopes > 3D Model. Here the user can consult the physical properties of each bar the program has taken into account for the analysis.

In the case of Example 1, the 0.25x0.5m beam has a free span of 4.5m, and so the weight transmitted to the columns is:

Wbeam = 4.5m x 0.25m x 0.5m x 24.525kN/m3 ( Wbeam = 13.795kN

Wcolumn = 2.5m x 0.5m x 0.5m x 24.525kN/m3 ( Wcolumn = 15.328kN

Wnode = 0.5m x 0.5m x 0.5m x 24.525kN/m3 ( Wnode = 3.066kN

N= 0.5 x Wbeam+ Wnode + Wcolumn ( N = 25.29kN

The X moment due to the dead loads is equal to the shear of the beam multiplied by the eccentricity (half the width of the column), minus the axial force of the beam multiplied by the distance to the total height of the column.

Mx = -0.5 x Wbeam x 0.25m + 0.83kN x 3m ( Mx = 0.76 kNm

Example 2 (10x10-1)

This example consists of four 0.6x0.6m separated 10m in both directions, with a 0.3x0.75m perimeter beam spanning between them. Spanning between the beams is a 0.3m deep flat slab. The floor height is set at 4m. No additional loads have been applied; only its self weight is present.

As was seen in the previous example, as the perimeter beams have been adjusted to the external faces of the columns, an eccentricity of 0.15m with respect to the columns is present.

The program transforms the slab into a mesh composed of bars separated at a distance of 0.25m so to discretise it. The self weight of the slab corresponds to the slab surface surrounded by the beams. This surface can be consulted at Groups ( Information about the group surface.

Wslab = 99.64m2 x 0.3m x 24.525kN/m3 ( Wslab = 733.10kN

Wbeam = 0.75m x 0.3m x 9.4m x 24.525kN/m3 ( Wbeam = 51.87kN

Wcolumn = 0.6m x 0.6m x 4m x 24.525kN/m3 ( Wcolumn = 35.316 kNAs the structure is symmetrical, the load distribution after the analysis is also symmetrical. Therefore the axial load descending the column can be taken as:

Ncolumn = 0.25 x Wslab + Wbeam + Wcolumn ( Ncolumn = 0.25 x 733.1 + 51.87 + 35.316 ( Ncolumn = 270.46kN

Regarding moments, CYPECAD automatically assigns a coefficient equal to 0.3 at the top of the column. If STAAD uses a coefficient equal to 1, the results provided by the programs will not match. This coefficient has to be modified using the option: Fixity coefficient at last floor. The Axial stiffness coefficient, which CYPECAD provides with a default value set at 2, also has to be modified otherwise the column shortening will not coincide with STAAD.

The default torsional stiffness reduction coefficients and Negative moment redistribution coefficients must also be modified as these values have been reduced in CYPECAD and can provide differences with STAAD.

Analysis using Metal 3D

The same example is analysed using a program similar to STAAD i.e. one which uses nodes and bars to model the structure with which the results can be compared. The program in question is Metal 3D: a bar and node program used to analyse steel, concrete, timber and aluminium structures.

A similar discretisation model as to what was used in CYPECAD is introduced. To check the generated discretisation model in CYPECAD, click on Envelopes > 3D Model.

In the model generated by CYPECAD, it can be appreciated that the program discretises the slab by generating a mesh with bars with a separation of 0.25m with the following physical properties:

The physical properties of the beams and columns are as follows:

When generating the bars, the program makes the slab bars that reach the column longer than the rest to ensure that these bars are fixed within the column and no force distortions arise in the rest of the bars which pass near the columns.

The bars of the slab are linked to the columns and beams at the geometric position at which they intersect. To simulate this link with Metal 3D, generic bars (link bars) with great stiffness will be used.

Discretisation used:

Now the model in Metal 3D can be introduced. The beams and columns are to be introduced as concrete bars measuring 30x75cm and 60x60cm respectively. The slab bars and link bars, between the beams and columns, shall be introduced as generic bars with the following properties:

Mechanical characteristics

MaterialRef.DescriptionA(cm)Avy(cm)Avz(cm)Iyy(cm4)Izz(cm4)It(cm4)

TypeDesignation

Concretef'c=200160 cm x 60 cm, (Rectangular)3600.003000.003000.001080000.001080000.001814400.00

230 cm x 75 cm, (Rectangular)2250.001875.001875.001054687.50168750.00498150.00

4Slab750.00750.00750.0058600.0039062.00112500.00

Notation:Ref.: ReferenceA: Area of the transverse sectionAvy: Shear area of the section in the local 'Y' axisAvz: Shear area of the section in the local 'Z' axisIyy: Inertia of the section about the local 'Y' axisIzz: Inertia of the section about the local 'Z' axisIt: Torsional inertiaThe mechanical characteristics of the elements correspond to those of their cross section at their mid-point.

The discretisation applied to the bars of the slab will be the same as the bar generation carried out by CYPECAD and introduced at an elevation of 4m. The beams are introduced at their exact position, i.e. with their axis displaced 15cm towards the outside of the slab and span between the external face of the columns; linking to the columns by means of a bar with great stiffness. The columns start at an elevation of 0m and reach elevation +3.25m, i.e. up to the bottom face of the beams. A bar with great stiffness is introduced from the top of the column to the beam intersection node to simulate the complete node.

Loads considered in the modelAs the density of the bars has been ignored, so not to duplicate the load, point loads are to be introduced on all the nodes of the slab equal to a 25x25cm segment of the slab:

Wslabnode = 0.25 x 0.25 x 0.3 x 24.525 = 0.46kN

Half of this load is applied at those nodes which are in contact with the edge beams, as the other half corresponds to the self weight of the beam.

Introduce a load at the top of the columns corresponding to the part of the column at the node:

Wcolumnnode = 0.6 x 0.6 x 0.75 x 24.525 = 6.62kN

The same model that has been introduced in Metal 3D is introduced in STAAD.

Beams and columns are introduced as 0.75x0.3m and 0.6x0.6m concrete bars respectively. For the slab bars, rectangular 0.3x0.25m bars are introduced, associated to the material Losa which has the same properties as concrete however its density has not been considered. For the bars with great stiffness, a generic bar, associated to the material RIGINF, and has been defined with the following properties:

The materials used and their properties are shown below:

The first load is the self weight of the columns and beams of the model. The second is a node load of 0.46kN in the Y axis, introduced for all the nodes of the slab. The third is a load of 0.23kN applied to all the perimeter nodes of the slab. The fourth and final load is another nodal load of 6.62kN introduced at the top nodes of the column bars.

Results

Forces at column starts